Algebraic Graph Theory

part of the Potsdam-Clarkson Summer Mathematics (REU) Program

REU 2016

E. Connelly, N. Grammel, M. Kraut, L. Serazo, C. Tamon. "Universality in Perfect State Transfer" Linear Algebra and Its Applications 531:516-532, 2017. arXiv: quant-ph:1701.04145.

REU 2015

Joshua Mundinger (Swarthmore College), Ethan Ackelsberg (Bard Colleg at Simon's Rock), C. Tamon (Clarkson), Zachary Brehm (SUNY Potsdam). Visiting speaker: Harmony Zhan (U Waterloo).

E. Ackelsberg, Z. Brehm, A. Chan, J. Mundinger, C. Tamon. "Laplacian State Transfer in Coronas" Linear Algebra and Its Applications 506:154-167, 2016. arXiv: math:co/1508.05458. E. Ackelsberg, Z. Brehm, A. Chan, J. Mundinger, C. Tamon. "Quantum State Transfer in Coronas" Electronic Journal of Combinatorics 24:2, P24, 2017. [link] arXiv: math:co/1605.05260. Pictures: hike to Mt. Jo, Mike Newman's talk, Lisa Hellerstein's talk. Trip to Summer Combo in Saint Michael's College: group photo. Ethan Ackelsberg gave a talk at MathFest 2015, August 5-8, 2015 in Washington, D.C. Updates: Ethan Ackelsberg (PhD student, Ohio State). Joshua Mundinger (PhD student, Chicago).

REU 2014

Ben Lovitz (Bates College), Rachael Alvir (Colorado Mesa), Sophia Dever (U Texas at Austin), James Myer (SUNY Potsdam), C. Tamon (Clarkson).

R. Alvir, S. Dever, B. Lovitz, J. Myer, C. Tamon, Y. Xu, H. Zhan, "Perfect State Transfer in Laplacian Quantum Walk" Journal of Algebraic Combinatorics 43:801-826, 2016. (A special issue dedicated to Chris Godsil) arXiv: quant-ph/1409.5840. Pictures: hike to Wright Peak. Ada Chan's talk. Gabriel Coutinho's visit: [1], [2]. Trip to Middlebury: group photo. Ben Lovitz gave a talk at MathFest 2014, August 6-9, Portland, Oregon. James Myer attended the Discrete Mathematics Day, Sept 20, Middlebury College, Vermont. Rachael Alvir and Sophia Dever gave a talk at Joint Mathematics Meetings in San Antonio, January 13, 2015. Music: "The PST Song (Safe Travels)," by James Myer. Updates: Rachael Alvir (PhD student, Notre Dame). Ben Lovitz (PhD student, University of Waterloo). James Myer (PhD student, CUNY Graduate Center).

REU 2013

Stephen Cameron (College of William and Mary), Sunrose Shrestha (Hamilton College), C. Tamon (Clarkson), Shannon Fehrenbach (University of Wisconsin at Oshkosh), Leah Granger (Clarkson), Oliver Hennigh (Clarkson).

S. Cameron, S. Fehrenbach, L. Granger, O. Hennigh, S. Shrestha, C. Tamon, "Universal State Transfer on Graphs" Linear Algebra and Its Applications 455:115-142, 2014. arXiv: quant-ph/1310.3885. Stephen Cameron gave a talk at YMC 2013 and at the AMS Special Session on "Quantum Walks, Quantum Computation, and Related Topics", Joint Mathematics Meetings, Baltimore, Maryland, January 18, 2014. Sunrose Shrestha gave a talk at SUMS 2013. Pictures: hike to Algonquin Mt; Chris Godsil's visit. Updates: Stephen Cameron (PhD student, University of Chicago). Leah Granger (PhD student, Chemical Engineering, North Carolina State University). Sunrose Shrestha (PhD student, Tufts). Oliver Hennigh (Air Force Lab, Rome, NY).

REU 2012

Standing: John Brown (SUNY Potsdam) [2nd from right], Devlin Mallory (UC Berkeley) [3rd from left], Abigail Raz (Wellesley) [4th from right].

J. Brown, C. Godsil, D. Mallory, A. Raz, C. Tamon, "Perfect State Transfer on Signed Graphs" Quantum Information and Computation 13(5&6):511-530, 2013. arXiv: quant-ph/1211.0505 D. Mallory, A. Raz, C. Tamon, T. Zaslavsky, "Which Exterior Powers are Balanced?" Electronic Journal of Combinatorics 20:2, P43, 2013. arXiv: math-co/1301.0973 John Brown, Devlin Mallory and Abigail Raz presented a poster at Summer Combo in Vermont, Saint Michael's College, Vermont. Devlin Mallory and Abigail Raz gave a talk at YMC 2012. Updates: John Brown (PhD student, Binghamton). Devlin Mallory (PhD student, University of Michigan). Abigail Raz (PhD student, Rutgers).

REU 2011

Left to right: Jessica Fuller (Seton Hall University), Eric Fredette (Clarkson), Andrew Tollefson (University of Nevada at Reno), Michael Landry (University of California at Berkeley), C. Tamon (Clarkson), Rachel Bachman (Clarkson).

R. Bachman, E. Fredette, J. Fuller, M. Landry, M. Opperman, C. Tamon, A. Tollefson, "Perfect state transfer on quotient graphs," Quantum Information and Computation 12(3&4):293-313, 2012. [pdf] Rachel Bachman gave a talk at MathFest 2011. Michael Landry gave a talk at YMC 2011. Jess Fuller gave a talk at CURM 2011. Updates: Rachel Bachman (teacher, Rocky Mountain School, Colorado). Jessica Fuller (PhD student, Emory). Michael Landry (PhD student, Yale).

REU 2010

Left to right: Oscar Perez (Hidalgo). Benjamin Greenberg (Grinnell), Yang Ge (Harvard), C. Tamon (Clarkson).

Y. Ge, B. Greenberg, O. Perez, C. Tamon, "Perfect state transfer, graph products and equitable partitions," International Journal of Quantum Information 9(3):823-842, 2011. [pdf] Benjy Greenberg gave a talk at YMC 2010. Some pictures from the event: 1 2 3 Updates: Yang Ge (MSc, Harvard, Applied Math & Statistics; current: Wall Street analyst).

REU 2009

Left to right: Matthew Russell (Taylor), Rachael Norton (Bowdoin), C. Tamon (Clarkson), Christopher Paribello (Clarkson), Ricardo Javier Angeles-Canul (Hidalgo).

R.J. Angeles-Canul, R. Norton, M. Opperman, C. Paribello, M. Russell, C. Tamon, "Perfect state transfer, integral circulants and join of graphs," Quantum Information and Computation 10(3&4):325-342, 2010. [pdf] R.J. Angeles-Canul, R. Norton, M. Opperman, C. Paribello, M. Russell, C. Tamon, "Quantum perfect state transfer in weighted join graphs," International Journal of Quantum Information 7(8):1429-1445, 2009. [pdf] Matthew Russell gave a talk at YMC 2009 (some pictures from the event: 1 2). Updates: Rachael Norton (PhD student, University of Iowa). Christopher Paribello (MSc, Clemson; current: MathWorks, Boston). Matthew Russell (PhD, Rutgers).

REU 2008

Left to right: Shawn Mead-Gluchacki (SUNY Potsdam), Markus Kliegl (Swarthmore), C. Tamon (Clarkson), Ana Best (McGill).

Ana Best, Markus Kliegl, Shawn Mead-Gluchacki, C. Tamon, "Mixing of Quantum Walk on Generalized Hypercubes," International Journal of Quantum Information 6(6):1135-1148, 2008. [pdf] [preprint] Picture from a hike at Debar Mountain, Meacham Lake, NY: 1 Updates: Ana Best (PhD student, McGill, statistics). Markus Kliegl (PhD, Chicago/Princeton). Shawn Mead-Gluchacki (PhD student, Syracuse).

REU 2007

Left to right: Leon Bergen (Swarthmore), Jennifer Lin (Princeton), C. Tamon (Clarkson), Dillon Ethier (Clarkson).

W. Adamczak, K. Andrew, L. Bergen, D. Ethier, P. Hernberg, J. Lin, and C. Tamon, "Non-uniform mixing of quantum walk on cycles," International Journal of Quantum Information 5(6):781-793, 2007. [pdf] [preprint] Note: this work is a combination of REUs 2003 and 2007. Jennifer Lin gave a talk at YMC 2007 (picture from the event: 1). Updates: Leon Bergen (PhD, MIT, in Philosophy and in Brain and Cognitive Sciences; postdoc, Stanford). Jennifer Lin (PhD, University of Chicago, physics). Dillon Ethier (PhD student, Rochester).

REU 2006

Left to right: C. Tamon (Clarkson), William Carlson (Kansas State University), Kathleen Wrobel (SUNY Potsdam), Julian Rosen (University of Oklahoma), Allison Ford (Mary Baldwin College); seated: Elizabeth Harris (SUNY Potsdam).

W. Carlson, A. Ford, E. Harris, J. Rosen, C. Tamon, K. Wrobel, "Universal Mixing of Quantum Walk on Graphs," Quantum Information and Computation 7(8):738-751, 2007. [pdf] [preprint] Updates: William Carlson (PhD student, University of Texas at Austin). Julian Rosen (Assistant Professor, Maine; PhD, University of Michigan; postdoc, University of Georgia, University of Waterloo).

REU 2005

Left to right: C. Tamon (Clarkson), Siddharth Rajaram (Middlebury College), Jeffrey Ward (Clarkson), Peter Lo (St. Mary's College), Daniel Sullivan (Swarthmore College), Diana Schepens (Houghton College).

P. Lo, S. Rajaram, D. Schepens, D. Sullivan, C. Tamon, J. Ward, "Mixing of Quantum Walk on Circulant Bunkbeds," Quantum Information and Computation 6(4&5), 370-381, 2006. [pdf] [preprint] P. Lo, S. Rajaram, D. Schepens, D. Sullivan, J. Ward, "Quantum Walks on Circulant Bunkbeds," poster prize, Undergraduate Student Poster Session, Joint Mathematical Meetings of the AMS/MAA, San Antonio, Texas, January 2006. Jeff Ward was our poster presenter (replacing Sid Rajaram). Updates: Peter Lo (MS, Towson University; math teacher). Sid Rajaram (PhD student, Boston University; MSc, Waterloo). Diana Schepens (PhD student, Montana State (MSc)). Daniel Sullivan (PhD student, University of Chicago, computer science (MSc)). Jeff Ward (NSA).

REU 2004

Left to right: Jacob McMillen (SUNY Fredonia), Jesse Clark-Stone (SUNY Potsdam), Jessica Etheredge (University of Southern Alabama), C. Tamon (Clarkson).

J. Clark-Stone, J. Etheredge, J. McMillen, C. Tamon, "On the Spectral Types of Circulants," draft. Updates: Jesse Clark-Stone (PhD student, Mathematics, Clarkson). Jacob McMillen (PhD student, Oregon State University; MSc, Emory).

REU 2003

Left to right: Kevin Andrew (Harvey Mudd College), William Adamczak (SUNY Albany), Peter Hernberg (SUNY Potsdam), C. Tamon (Clarkson).

W. Adamczak, K. Andrew, P. Hernberg, C. Tamon, "A note on graphs resistant to quantum uniform mixing," poster, 7th Workshop on Quantum Information Processing, Waterloo, Canada, January 2004. [preprint] Updates: William Adamczak (PhD, Albany; visiting faculty, Siena College). Kevin Andrew (analyst, Milliman; Dominican Friars). Peter Hernberg (PhD student, Univ. Oregon).

REU 2002

Left to right: C. Tamon (Clarkson), Ryan Belk (SUNY Binghamton), Amir Ahmadi (Clarkson), Carolyn Wendler (Kenyon College).

A. Ahmadi, R. Belk, C. Tamon, C. Wendler, "On Mixing in Continuous-time Quantum Walks on Some Circulant Graphs," Quantum Information and Computation 3(6) 611-618, 2003. [pdf] [preprint] Updates: Amir Ahmadi (PhD, Georgia Tech, Chemical and Biomolecular Engineering). Ryan Belk (Georgetown, Law). Carolyn Wendler (MSc, University of Illinois at Urbana-Champaign; math teacher).

REU 2001

Left to right: Amarda Shehu (Clarkson), Hester Graves (Wellesley College), Sarah Good (University of Washington), Matthew Day (University of Texas at Austin), Catherine Vanderwaart (Swarthmore College), C. Tamon (Clarkson).

M. Day, S. Good, H. Graves, A. Shehu, C. Vanderwaart, "On Totally Shattered and Hyperuniversal Graphs," poster prize, Undergraduate Student Poster Session, AMS-MAA Joint Mathematics meeting, January 2002, San Diego, California. Manuscript: [pdf] Updates: Matthew Day (Faculty, Arkansas; Postdoc, CalTech; PhD, Chicago). Sarah Good (U.S. Air Force). Hester Graves (Postdoc, Queens; PhD, Michigan). Amarda Shehu (Faculty, George Mason University; PhD, Computer Science, Rice). Catherine Vanderwaart (MS, MIT, Transit Lab).